llmnl: Evaluate Log Likelihood for Multinomial Logit Model
Description
llmnl evaluates log-likelihood for the multinomial logit model.
Usage
llmnl(beta,y, X)
Arguments
beta
k x 1 coefficient vector
y
n x 1 vector of obs on y (1,…, p)
X
n*p x k Design matrix (use createX to make)
Value
value of log-likelihood (sum of log prob of observed multinomial outcomes).
Warning
This routine is a utility routine that does not check the
input arguments for proper dimensions and type.
Details
Let \(\mu_i=X_i beta\), then \(Pr(y_i=j) = exp(\mu_{i,j})/\sum_kexp(\mu_{i,k})\).
\(X_i\) is the submatrix of X corresponding to the
ith observation. X has n*p rows.